Multiple choice

If $\sec 4A = cosec (A-20^{\small\circ})$, where $4A$ is an acute angle, find the value of $A$.

  1. $A = 32^{\small\circ}$
  2. $A = 22^{\small\circ}$
  3. $A = 41^{\small\circ}$
  4. $A = 16^{\small\circ}$
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B Correct answer
Explanation

Using the identity sec(x) = cosec(90 - x), we set 90 - 4A = A - 20. Solving for A gives 5A = 110, so A = 22 degrees.

AI explanation

Apply the co-function identity sec x equals cosec(90 degrees minus x) to rewrite the left side as cosec(90 degrees minus 4A). Equating the angles gives 90 degrees minus 4A equals A minus 20 degrees. Solving this linear equation results in 5A equals 110 degrees, so A equals 22 degrees.

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